Their 23-year-old soldier son Gordon telephoned them from Iraq a couple of weeks ago to say he was OK.
For four long weeks before and during the war, the Alexanders had not heard from their son, who serves with the British army.
Both say they are very happy their son is fine, and that he will be leaving Iraq and returning to his base in Germany in the next couple of weeks.
"I'm really relieved," says David Alexander. "I'm just happy it's over."
Lilia Alexander also says she's very relieved her son is safe.
"I was very, very happy when he phoned."
Both David and Lilia also say they are proud of their son.
Gordon Alexander is a trooper in the Royal Scots Dragoon Guards, in which he drives a Challenger tank.
His father says Gordon didn't offer too many details about his battlefield experiences, other than to say there had been one or two rough spots.
Several mortar shells exploded around his son's tank, David says.
"A few bullets were zinging off his tank."
The elder Alexander believes the experience will sink in more for his son when he leaves Iraq and he may talk more about it when they see each other again.
The young soldier may be visiting Hay River in June during some time off.
For now, Gordon Alexander is helping guard an airfield just outside the southern Iraqi city of Basra.
"He can relax to a certain extent," says David.
"I think he's looking forward to coming home."
In fact, David says his son is a little bored now in Iraq, and is getting tired of the flies and the heat.
Since that first call, Gordon and his parents have spoken a couple of more times, even though soldiers have to line up for access to a telephone.
Next up for Gordon is a tour of duty as a peacekeeper in Northern Ireland, probably in November or December.
Gordon - who has dual British and Canadian citizenship - spent 13 years in Hay River before joining the British forces in 2001, and he considers the town his home.